Question

Представь многочлен 216+ 108s+ 18s^2+ s^3 виде куба двучлена

Answer 1

Ответ:

~~~~~~~~~~~~~~~~~~~~~~~~~~

Answer 2

Factoring a Polynomial into the Cube of a Binomial

To express the polynomial \(216 - 108s + 18s^2 + s^3\) as the cube of a binomial, we can use the following steps:

1. Identify the Leading Term: The leading term of the polynomial is \(s^3\). 2. Use the Cube of a Binomial Formula: The cube of a binomial formula is \((a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3\). 3. Match the Terms: We need to match the terms of the given polynomial with the terms of the cube of a binomial formula.

Applying the Cube of a Binomial Formula

Let's apply the cube of a binomial formula to express the given polynomial as the cube of a binomial:

The given polynomial: \(216 - 108s + 18s^2 + s^3\)

Using the cube of a binomial formula \((a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3\), we can match the terms as follows:

- \(216 = a^3\) - \(-108s = 3a^2b\) - \(18s^2 = 3ab^2\) - \(s^3 = b^3\)

Solving for the Binomial

By matching the terms, we can solve for the binomial:

- From \(216 = a^3\), we find that \(a = 6\). - From \(-108s = 3a^2b\), we find that \(b = -2s\).

Therefore, the binomial is \((6 - 2s)\).

Conclusion

The polynomial \(216 - 108s + 18s^2 + s^3\) can be expressed as the cube of the binomial \((6 - 2s)\).